I'm trying to figure out how to handle my financial assets prior to declaring them for law school financial aid purposes. Is it worth giving away money, or similarly not accepting money, for the purpose of minimizing expected personal contribution?

It looks like this is really only pertinent for HYS. Are you a competitive applicant for those schools? For the majority of schools expected personal contribution is irrelevant - you get merit aid or you take out loans (which you can get regardless of your financial situation, assuming your credit is fine).

I don't have any personal familiarity with how their financial aid works. My understanding is that HYS do take assets into consideration when calculating aid (for instance, if you work a high-paid job over the summer your aid for the following year is reduced), but I don't know how exactly (how assets play into this versus income) or what the best method of handling this is. FWIW, their need-based aid is capped so even someone with the max need-based aid will be taking some loans to cover the cost of attendance.

H will assess a contribution of essentially all personal assets for need-based aid. The amount is divided evenly over three years so that your annual contribution will be 1/3 of of your assets at the time of your financial aid application, sans a small emergency allowance.

So there is, in some circumstances, an incentive to spend down assets between now and the date of your financial aid application, although for obvious reasons this isn't advisable for the vast majority of people (not guaranteed admission, uncertainties of if you will qualify for grant aid and how much your financial aid award might be, whether some or all of your projected grant aid ends up being an institutional loan instead, etc.)

Info about H's treatment of students' personal assets for financial aid is available here.